Sequenced Bone Movement with IK
Here is my solution (Some description): I have 4 horizontal bones(small red one IK_Target), they all have a 'Limit Distance' constraint to each other. Moving IK_TRGT causes the bones to come out one at a time - that gets the action you require. The rest is just 2 sets of bones parented to each other(yellow to purple), yellow bones have IK targeting the purple bone in front of it which is parented to its corresponding larger horizontal bone. I have them all stacked on top each other when built, that can be fixed last to get some offset.Forgot to mention if this rig is going to traverse the Scene it will need a ParentBone to avoid unwanted transforms.
 

DISCLAIMER: This file created in v2.76 - If using 2.7x it will open fine,, If using 2.8x 'APPEND' the objects from the 'Object' folder.